A two-cycle engine is in a wide use for portable engine-driven work machines for which compactness, lightness and high power are required. High power and fuel-efficiency are required for the two-cycle engine. However, a problem of low power and increased exhaust gas occurs to the two-cycle engine when fresh gas escapes through an exhaust hole during exhaust and scavenge. In order to avoid this problem, there has been proposed a system in which the number or shape of scavenge hole or exhaust hole is devised, or a layered scavenging system in which air is guided first.